Solve the system of linear equations using matrices.
2x+y+z=3
-x+y-6z=-24
x+6y+6z=-4
The solution is ____ (Type an exact answer in simplified form.)
Answer:
(x, y, z) = (2, -4, 3)
Step-by-step explanation:
It is convenient to let an appropriate calculator reduce the augmented matrix to reduced row-echelon form. The rightmost column in that form is the solution vector [x, y, z].
__
If you want to solve this by hand, you can perform the following row operations to reduce the augmented matrix as shown in the attachment.
r1 ← r2 +r3; r2 ← (r2 +r3)/7 . . . . use this matrix for the next row replacement
r3 ← (r3 -r1 -4·r2)/11 . . . . . . . . . . use this matrix for the next row replacement
r1 ← r1 -2·r2 +5·r3
__
r1, r2, r3 refer to rows 1, 2, 3, respectively. The indicated multiplication and division are scalar operations, operating on each individual term in the row.
_____
Additional comment
Most graphing calculators have matrix solving functions. Apps are available for phone and tablet that will do this, and there are online websites that will reduce an augmented matrix as well.
A set of house plans is made in the ratio 30:1. if a room is 6m long,how long is this room on the plan
Answer:
0.2
Step-by-step explanation:
30: 1
6:?
cross multiply
(6*1)/30
ans:0.2cm
A bag of sugar weighs 6²/⁵. What is the weight of 6¹/⁴ of such bag?
How many two thirds are there in 4¹/³?
Answer:
6 and a half 2 thirds are in 4 1/3
Step-by-step explanation:
2/3x=13/3
2x=13
x=6.5
/////////////////////////
Answer:
E. 945Step-by-step explanation:
The shortest root is when you go to next level down at each move.
From the black triangle you can move to 3 triangles below. The level below has 5, then 7, then 9 triangles.
The number of shortest roots is:
3*5*7*9 = 945Correct choice is E
1. Two linear functions are shown below. Which function has the greater rate of change? Function A Function B 10 у y 4 32 8 8 6 44 12 4 56 2 16 68 Х 0 20 80 0 2 4 6
Answer:
I don't understand clear ur question
Solve |x – 4| + 6 = 17.
A. x = 15 and x = -7
B. x = 15 and x = -15
C. x =-15 and x = -7
D. x = -15 and x = 7
Answer:
A
Step-by-step explanation:
15 and -7
|x-4|=17-6
|x-4|=11
x-4=11
x-4=-11
x=11+4
x=15
x=-11+4
x=-7
i need help on this math problem
Answer:
I can't see the problem I am blind but still very hard to see it's not quite clear
Write an equation of a line with an x-coefficient of - 3 and a y-intercept of 7
Answer:
y = -3x + 7
Step-by-step explanation:
For an equation in the format y = ax + b, a is the coefficient of x, and b is the y intercept.
sole the inequality x-8>-4
Answer:
[tex]x>4[/tex]
Based on this, we know the correct number line will be an empty bubble with a line going to the right of 4.
Step-by-step explanation:
[tex]x-8>-4[/tex]
add 8 to both sides of the inequality
[tex]x>4[/tex]
8x-2y=18 3x-y=5 What is the y value of the solution?
Answer:
y = 7
Step-by-step explanation:
8x - 2y = 18
3x - y = 5
the above system of equations can be solved by multiplying the second equation by -2 so the 'y-terms' get eliminated
you can then substitute the value of 'x' into the equation to find the value of 'y'
8x - 2y = 18
+ -6x + 2y = -10
2x = 8
x = 4
3(4) - y = 5
12 - y = 5
-y = -7
divide each side by -1 to get: y = 7
An eight-sided dice numbered from 1 to 8 is rolled 80 times to determine whether it is fair, a If the dice is fair, how many of each number would you expect to get?
Answer:
10 times for each number
Step-by-step explanation:
:)
Answer:
10
Step-by-step explanation:
if the dice is fair, the sides will land one time every 8, so if its rolled 80 time, and it was equal 10 would be your answer.
Your neighbour has two children. You learn that he has a son, Samuel. What is the probability that Samuel's sibling is a brother?
Answer: 50%
Step-by-step explanation:
If the neighbor has 2 children and one is a male out of 100% it would just be 100% divided by 2 i think im not sure but i hope this helps
At a coffee shop, a latte costs $5.50 and
hot tea costs $1.75. Each day, Parker
buys 2 hot teas and several lattes for
his office staff. Which equation can be
used to find y, Parker's total cost, if x
represents the number of lattes? (7.1A,
7.1B, 7.1D, 7.1F)
A y = 5.50x + 3.50
BY 5.50x + 1.75
C y = 1.75x + 5.50
Dy = 3.50x + 5.50
Answer:
A) y = 5.50x + 3.50
Step-by-step explanation:
2 x 1.75 = 3.50 + x number of lattes $5.50 each.
Mr. And mrs. Samson decide to go with design a and purchase the materials. Their total bill is 356.88. If they pay 220 in cash and charge the remainder, how much did they charge?
Answer:
136.88
Step-by-step explanation:
Subtract 356.88 - 220 = 136.88
HELP!!!!! FAST!!!!! !!!!!!!!!!!!!!!!!!!!!!
Answer:
37
Step-by-step explanation:
I don't know if this is totally correct
ATQ,
★⤿ 8(x+9) ≥ 224
★⤿ x+9 ≥ 224/8
★⤿ x +9 ≥ 28
★⤿ x ≥ 28-9
★⤿ x ≥ 19
Hence , option A is correct ✓
For each of the solutions of the equations find two consecutive integers between which the solution is located: x^2=3, x^2=5
The two consecutive integers between which the solution is located are 1 and 2
The two consecutive integers between which the solution is located are 2 and 3
Given the expressions x^2 = 3 and x^2 = 5
For the equation
x^2 = 3
Take the square root of both sides
x = ±√3
x = 1.732
Hence the two consecutive integers between which the solution is located are 1 and 2
For the expression
x^2 = 5
x = ±√5
x= 2.24
The two consecutive integers between which the solution is located are 2 and 3
learn more on roots here:https://brainly.com/question/12501796
Answer:
1. 1,2 2. 2,3
Step-by-step explanation:
List all the factors pairs in the table 64
(1, 64), (2, 32), (4, 16), (8, 8).
Answer:
1 x 64
2 x 32
4 x 16
8 x 8
Step-by-step explanation:
Factors of 64: 1, 2, 4, 8, 16, 32 and 64.
Pairs:
1 x 64
2 x 32
4 x 16
8 x 8
Hope this helps :)
Which equation could be represented by the number line?
[tex]Hiya![/tex]
Sokka is here to help!!
I believe it is D..
Hopefully, this helps you!
[tex]Sokka[/tex]
Answer:
I think it is C.
Step-by-step explanation:
It has a starting point. It also has an arrow that is going toward the negatives. It also has a gap of 9 units. So therefore, C is our answer.
Which is the algebraic expression for "two times the sum of a number and four'?
*Someone save me.*
Answer:
2(x+4)
Step-by-step explanation:
How to do question 1 ?
Step-by-step explanation:
srry
Answer:
A
Step-by-step explanation:
I DID THE WORK IN MY HEAD
btw im 11
25 points! Help (Vectors)
Answer:
[tex]7\cos(30^{\circ})[/tex]
Step-by-step explanation:
Hi guys mind helping me with this
Answer:
i actually have the same question
Step-by-step explanation:
Answer:
the bearing is 290°
Step-by-step explanation:
firstly complete those compass directions (just to make it easier for you). find the remaining angle on A which is 110°. subtract 90° from it and get 20°. using the concept of alternating angles. then add from the North to where the line connecting B n A is, 270°+20°=290°
Which of the following inequality’s matches the graph? A: x ≤ 5 B: x ≥ 5 C: y ≤ 5 D: y ≥ 5 what is the answer
Answer: Choice A
[tex]x \le 5[/tex]
========================================
Explanation:
Any point in the shaded purple region has an x coordinate that is 5 or smaller. So we go for [tex]x \le 5[/tex]. Either x = 5 or x < 5. The boundary line is solid to indicate that points on the boundary are included in the solution set.
plz answer this with complete process plzzz I will give you brainlist ..........
Answer:
Step-by-step explanation:
Needs a picture to be solved, please put one.
Answer:
i know
Step-by-step explanation:
I know have a amazing day
The low temperature on a certain day is 56°F. The low temperature is 14°F lower than the high temperature, h. Which equation can be used to find the high temperature for that day? o 56 = h – 14 Oh + 56 = 14 O 56 = 14h 0 56 = h + 14 WHOEVER ANSWER GETS BRAINLESS NEED HELP
Answer: 1.09
Step-by-step explanation:
Evaluate the expression -2
Answer: 2x for x=3: 2(3) = 6.
Step-by-step explanation:
-6/5 - (-3/8)
Help please
Answer:
-0.825
Step-by-step explanation:
Did not know the options so do not know if this is right or not.
Here is ur answer.
- BRAINLIEST answerer
Which graph shows all natural numbers less than 3?
Answer:
graph A shows all natural numbers less than 3
Step-by-step explanation:
Answer:
The Answer Is B
Step-by-step explanation:
A car can go 420 miles on a tank of gas (15 gallons in a tank). How many kilometers can this car go on 6.5 gallons
Answer:
182 miles
Step-by-step explanation:
15 gallons ------------------------- 420 miles
1 gallons --------------------------- 420/15 miles
1 gallons --------------------------- 28 miles
6.5 gallons -------------------------- 6.5 × 28 miles
6.5 gallons -------------------------- 182 miles
The car can go 182 miles on 6.5 gallons.
It is given that the a car can go 420 miles on a tank of gas of 15 gallons in a tank.
It is required to find the how many kilometers can this car go on 6.5 gallons.
What is a fraction?Fraction number consists of two parts one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called denominator.
We have a car can go 420 miles on 15 gallons gas.
A car can go on 1 gallon = [tex]\frac{420}{15}[/tex] = 28 miles ie.
A car can go on 1 gallon = 28 miles
On 6.5 gallons car can go = 6.5×28
= 182 miles
Thus, the car can go 182 miles on 6.5 gallons.
Learn more about the fraction here:
brainly.com/question/1301963
If
x
=
4
and
y
=
6
, evaluate the following expression:
2
(
x
+
y
)
[tex]x=4 , ~y = 6\\\\2(x+y) = 2(4+6) = 2(10) = 20[/tex]